After work we went out and started on the hot tub. I undid the heat sensor (that was caulked in!), then cut the sensor off the wire while Vic plugged the hole, then I plugged the hole while she taped the new wire to the old wire and pulled it through. Then I screwed the new sensor (with it's la-di-da O ring) in, and went to wire it to the connector. Here's where I discovered that it looks like there was possibly nothing wrong with the old one - the wires didn't look to be pushed in properly, and I'm betting that the controller fails to a high temperature when it's getting an intermittent read. Bugger - still, I've cut the old wire, and the new one's fitted. On turning the power back on, it read 88F, which is probably a lot closer to the truth than the 118F the old sensor was reading. Yay.
We went out to get something to eat to celebrate, and so Vic could show me a local house that's decorated with spiders for Hallowe'en. Some people here really get into their holidays :o)